Where you travel in any part of the country depends on what your interests are and how many stops you want to make along the way.
There are two entry points into Alberta from the state of Montana, one at Coutts on Highway 15 and one at Carway on Highway 89. No visit to this part of the country would be complete without a visit to Glacier National Park and particularly the "Going to the Sun" highway, you can access this wonder of construction from either the West or East end of the park, there are camping areas near both entrances but you "cannot" take a trailer over this road and pass. Absolutely worth the visit.
From Glacier I would enter Alberta at Coutts and make my first stop at "Writing on Stone Provincial Park and Heritage site" -
http://travelalberta.com/Places%20to...al%20Park.aspx - If you have any interest in the history of Native Americans in particular the Blackfoot and Shoshone this is a must stop, the information center is grand and the hoodoo's are a natural wonder. The area is also home to the largest remaining native grasslands in Canada and perhaps North America.
From there travel on to Waterton National Park, this is an extension of Glacier National Park established in conjunction with the US and Canadian Governments. There are 3 campgrounds in the area, one within the townsite and two within a short drive of the park entrance. You will be required to purchase a pass for visits to our National Parks as in the USA.
Again if First Nations history is of interest you should head north from Waterton to Fort McLeod and visit "Head Smashed In Buffalo Jump" world heritage site. It is the largest preserved site of it's kind in North America -
http://www.history.alberta.ca/headsmashedin/ Even if your interests are not of early history this site is worth the visit.
Calgary, well what can I say, the Stampede is unique in it's size and grandeur but not for everyone, the rest of Calgary is just another city (sorry to the natives but I lived there for many years) So head west and visit Banff and Lake Louise, then head north on the Glacier Parkway and visit Jasper and area. You can head east from Jasper to Edmonton and if "BIG" malls are your thing then visit West Edmonton Mall, otherwise you will just see another city (yup lived here too). Go South from Edmonton and make a stop in Drumheller if you are into really old things like Dinosaurs and the like.
Nothing North of Edmonton except sandy oil and destruction.
Now if you decide to venture into British Columbia, then that is a whole "nother" story and adventure I won't go into.
Don't bring a handgun with you as has already been mentioned, you will not be allowed to take it with you, unless you plan to hunt why bring a gun of any kind, we still use bows and arrows up here in the frozen north. (Yup I have hunted all my life and do own a handgun)
Most importantly come and meet some of your neighbors, you might even like some of us and do bring lots of money we are a developing country still and need the help.....Have a wonderful trip.